Answered: Use the standard normal distribution or…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Use the standard normal distribution or the t-distribution to construct a

90%

confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results.

In a random sample of

mortgage institutions, the mean interest rate was

3.57%

and the standard deviation was

0.38%.

Assume the interest rates are normally distributed.

Which distribution should be used to construct the confidence interval?

Use a normal distribution because

n<30

and the interest rates are normally distributed.

Use a t-distribution because the interest rates are normally distributed and

is known.

Use a normal distribution because the interest rates are normally distributed and

is known.

Use a t-distribution because it is a random sample,

is unknown, and the interest rates are normally distributed.

Cannot use the standard normal distribution or the t-distribution because

is unknown,

n<30,

and the interest rates are not normally distributed.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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